Question

find the center and radius of the circle defined by the equation ((x + 5)^2 + (y + 8)^2 = 25).
center: ((square, square))
radius: (square)
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Explanation:

Step1: Recall the standard circle equation

The standard form of a circle's equation is \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius.

Step2: Identify \(h\), \(k\), and \(r\) from the given equation

Given the equation \((x + 5)^2 + (y + 8)^2 = 25\), we can rewrite it as \((x - (-5))^2 + (y - (-8))^2 = 5^2\). By comparing with the standard form, we find that \(h = -5\), \(k = -8\), and \(r = 5\).

Answer:

center: \((-5, -8)\)
radius: \(5\)